Question

Using the quadratic formula to solve x2 = 5 – X, what are the values of X?
-1021
2
-1 + 19
2
5+21
2
1+ /19/
2

Answer 1

Answer:

$A)\:x=\frac{-1\pm\sqrt{21}}{2}$

Step-by-step explanation:

$x^2=5-x$

Add x from both sides:

$\longmapsto$ $x^2+x=5-x+x$

$\longmapsto$ $x^2+x=5$

Subtract 5 from both sides:

$\longmapsto$ $x^2+x-5=5-5$

$\longmapsto$ $x^2+x-5=0$

Now, we'll use the quadratic formula to solve this problem: $x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\longmapsto$ $x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\times \:1\cdot \left(-5\right)}}{2\times \:1}$

$\longmapsto$ $\sqrt{1^2-4\times \:1\times \left(-5\right)}$

$\longmapsto$ $1^2=1$

$\longmapsto$ $\sqrt{1+4\times \:1\times \:5}$

Multiply 4*1*5= 20

$\longmapsto$ $\sqrt{1+20}$

Add 1 and 20= 21

$\longmapsto$ $\sqrt{21}$

$\longmapsto$ $x_{1,\:2}=\frac{-1\pm \sqrt{21}}{2\times \:1}$

$\longmapsto$ $x_1=\frac{-1+\sqrt{21}}{2\times \:1}$

$\longmapsto$ $\frac{-1+\sqrt{21}}{2\times \:1}$

Multiply 2 and 1= 2

$\longmapsto$ $\frac{-1+\sqrt{21}}{2}$

$\longmapsto$ $x_2=\frac{-1-\sqrt{21}}{2\times \:1}$

$\longmapsto$ $\frac{-1-\sqrt{21}}{2\times \:1}$

Multiply 2 and 1= 2

$\longmapsto$ $\frac{-1-\sqrt{21}}{2}$

$\longmapsto$ $x=\frac{-1+\sqrt{21}}{2},\:x=\frac{-1-\sqrt{21}}{2}$

$\hookrightarrow$ $x=\frac{-1\pm\sqrt{21}}{2}$

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